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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 12 April 2023, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Let λ∈Z\lambda\in\mathbb{Z}, a⃗=λi^+j^−k^\vec{a}=\lambda\hat{i}+\hat{j}-\hat{k} and b⃗=3i^−j^+2k^\vec{b}=3\hat{i}-\hat{j}+2\hat{k}. Let c⃗\vec{c} be a vector such that (a⃗+b⃗+c⃗)×c⃗=0⃗(\vec{a}+\vec{b}+\vec{c})\times\vec{c}=\vec{0}, a⃗⋅c⃗=−17\vec{a}\cdot\vec{c}=-17 and b⃗⋅c⃗=−20\vec{b}\cdot\vec{c}=-20. Then ∣c⃗×(λi^+j^+k^)∣2\left|\vec{c}\times(\lambda\hat{i}+\hat{j}+\hat{k})\right|^2 is equal to
  1. (1)4646Official answer
  2. (2)4949
  3. (3)5353
  4. (4)6262

Official answer

Option 1

NTA final key.

Chapter
Vector Algebra
Topic
Cross Product
Idea tested
Condition for Parallel Vectors

Same idea in other shifts

Asked 2× in all
  1. 3 Apr 2025, Shift 1 · Q24Let a⃗=i^+j^+k^,b⃗=3i^+2j^−k^,c⃗=λj^+μk^\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 3\hat{i} + 2\hat{j} - \hat{k}, \vec{c} = \lambda\hat{j} + \mu\hat{k} and d^\hat{d}…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.